IMO the key to doing it right is ensuring that your hosted solution actually provides value: either because its difficult to operate at scale, there are certain regulatory/compliance requirements that need to be met, because certain features are restricted to a hosted product or under an enterprise license, etc.
I've seen a decent number of people create a hosted version of their product, slap SAML/SSO behind an "enterprise" plan, and wonder why nobody their successful OSS product doesn't translate to meaningful hosted revenue.
You can test and use the software for free
Companies can outsource the responsibility of hosting.
In the long term, maybe. In the short to medium term, most of the development ends up being done by the company who created the project.
I guess for simple stuff like typo bugs, people will submit PRs, and maybe organisations with weird use-cases will merge their integrations etc into the project, though.